Analysis of Petrol Prices in Australia

This study analyzes the historical petrol prices in Australia based on different service station brands. It includes descriptive statistics, hypothesis testing, and post hoc analysis.

Statistics and data analysis
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10th May 2019

1. Section 1: Introduction
Brief introduction
This study sought to analyze the historical petrol prices in Australia. The analysis
focusses on looking at the petrol prices based on the different service station brands. The
data being utilized is for the September 2016 period. According to ACCC (2018), petrol
prices greatly vary in Australia based on the service station brand with Coles Express
brand being rated the most expensive in major cities in Australia. With this in mind, this
study sought to analyze and understand the average petrol prices in Australia with a focus
on comparing four selected service station brands (Caltex Woolworths, Caltex, 7-Eleven
and Coles Express).
Dataset 1
This dataset is a secondary data obtained from the government database that stores
historical prices of fuel in the country. The dataset contains a number of variables. The
cases involved are both quantitative and qualitative with ratio and nominal measurements
respectively. The table below gives the description of cases;
The description of the variables used is given in table 1 below;
Table 1: Description of the variables
Variable
name
Type of variable Measurement
Address Qualitative Nominal
Suburb Qualitative Nominal
Postcode Qualitative Nominal
Brand Qualitative Nominal
FuelCode Qualitative Nominal
Price Quantitative Ratio

This dataset comprised of 1000 cases, that is, this dataset consists of a sample size of
1000 cases.
Dataset 2
Data was collected by emailing the KOI students through SurveyMonkey. The students
were required to fill in a structured questionnaire related with service station they prefer
to buy petrol. This dataset is a primary data since the data is obtained directly from the
subjects. The limitation of this method of collecting data is that some students will fail to
respond to the survey. The data is also subject to bias as only those students who will
access the internet will be able to respond. The dataset contains three variables, namely;
age of the student, gender of the student and their preferred service station when it comes
to buying petrol. The cases involved are both qualitative and quantitative with ratio and
nominal measurements respectively. The table below gives the description of cases;
Table 2: Description of the variables
Variable name Type of variable Measurement
Age Quantitative Ratio
Gender Qualitative Nominal
Preferred station Qualitative Nominal
This dataset comprised of 50 cases, that is, a sample size of 50 students was selected for
this study.
2. Section 2: Analysis of single variable in Dataset 1.
This section presents the descriptive (summary) statistics for the variable price. From the
table, we can see that the average price of petrol is 122.50 while the median price is
121.95. The median and the mean are close to each other suggesting that the data could
possibly by symmetrical (following a normal distribution). Looking at the standard

deviation, we can see that the data is not widely spread out from the mean as the value is
much lower than the mean (SD = 13.49). Also considering the skewness value, we can
see that the value is -0.46 (a value that is closer to zero), which shows that the
distribution of price of petrol is close to a normal distribution (symmetrical).
Table 3: Descriptive statistics
Price
Mean 122.50
Standard Error 0.43
Median 121.95
Mode 129.90
Standard
Deviation 13.49
Sample Variance 181.86
Kurtosis 1.90
Skewness -0.46
Range 108.80
Minimum 57.90
Maximum 166.70
Sum
122496.5
0
Count 1000
The figure below (figure 1) presents the histogram for the petrol prices. As can be seen,
the histogram further confirms that the distribution of petrol prices closely follows a
normal distribution (the histogram has a bell-shaped curve).

Figure 1: Histogram for the petrol prices
This study sought to answer the research question “Is the average price of petrol is in all
service station in September 2016 is more than 115 Australian cents?” To answer this
research question, the following hypothesis was to be tested;
Null hypothesis (H0): The average price of petrol is in all service station in September
2016 is not significantly different from 115 Australian cents.
Alternative hypothesis (HA): The average price of petrol is in all service station in
September 2016 is significantly more than 115 Australian cents.
This hypothesis could also be written in symbol form as follows;
H0 : μ=115
H A : μ>115
To test this hypothesis, a one-sample t-test was performed. The results of the one-sample
t-test are given below;
Table 4: One-Sample Statistics
N Mean Std. Deviation Std. Error Mean

Price 1000 122.4965 13.48545 .42645
Table 5: One-Sample Test
Test Value = 115
t df Sig. (2-tailed) Mean
Difference
95% Confidence Interval of the
Difference
Lower Upper
Price 17.579 999 .000 7.49650 6.6597 8.3333
From table 4 above, we can see that the average petrol price for 2016 was 12250 (SD =
13.48, N = 1000). Also from table 5, we can see that the p-value of the one-sample t-test
is 0.000 (a value less than 5% level of significance), we therefore reject the null
hypothesis and conclude that the average price of petrol is in all service station in
September 2016 is significantly more than 115 Australian cents.
3. Section 3: Analysis of two variables in Dataset 1
Numerical summary
Table 6 below presents the summary statistics for the four selected brands. As can be
seen, the brand with the highest mean was the Coles Express brand (M = 124.72, SD =
13.05, N = 86), it was closely followed by the Caltex brand (M = 124.08, SD = 14.16, N
= 382), the third most expensive brand was the 7-Eleven brand (M = 121.14, SD = 12.00,
N = 171) and the least expensive brand was the Caltex Woolworths brand (M = 120.39,
SD = 14.82, N = 110).
Table 6: Descriptive statistics on average price at different service stations
N Mean Std.
Deviation
Std. Error 95% Confidence Interval
for Mean
Minimum Maximum

Lower
Bound
Upper
Bound
Caltex 382 124.082
5
14.15816 .72439 122.6581 125.5068 60.90 166.70
Caltex
Woolworths
110 120.386
4
14.82110 1.41314 117.5856 123.1872 57.90 149.90
Coles Express 86 124.720
9
13.05159 1.40739 121.9227 127.5192 99.90 152.90
7-Eleven 171 121.141
5
11.99533 .91731 119.3307 122.9523 99.90 147.90
Total 749 122.941
5
13.74414 .50220 121.9556 123.9274 57.90 166.70
Figure 2 below presents the mean plot to represent the average price for the four brands.
This figure further clearly shows the average prices of the different brands and as can be
seen, Coles Express is riding top of all the four brands while Caltex Woolworths is at the
bottom. This gives a very clear visualization of how the average petrol prices compare in
all the four selected brands.
Figure 2: Mean plot for the petrol price based on brand
Hypothesis test

In this section, we sought to test whether the petrol prices vary across the four brands
(Caltex, Caltex Woolworths, Coles Express and 7-Eleven). The following hypothesis was
tested;
Null hypothesis (H0): There is no significant difference in the mean petrol prices for the
four brands.
Alternative hypothesis (HA): At least one of the brands has significantly different mean.
To test this, a one-way analysis of variance (ANOVA) was performed at a 5% level of
significance. Results are presented below;
Table 7: Test of Homogeneity of Variances
Price
Levene Statistic df1 df2 Sig.
.786 3 745 .502
Table 7 above shows the results of the homogeneity of variances test. As can be seen, the
assumption of homogeneity of variance (equal variances) is held as the null hypothesis is
not rejected (p < 0.05).
Table 8: ANOVA
Price
Sum of Squares df Mean Square F Sig.
Between Groups 2041.779 3 680.593 3.641 .013
Within Groups 139256.420 745 186.921
Total 141298.199 748
From table 8 above, we can see that the null hypothesis is rejected (p < 0.05). By
rejecting the null hypothesis we conclude that at least one of the brands has significantly
different mean.
Post hoc analysis test

A post hoc analysis test using LSD test was performed to identify which of the brands
had significantly different mean petrol prices. The results are presented in table 9 below.
Table 9: Multiple Comparisons
Dependent Variable: Price
LSD
(I) Brand (J) Brand Mean
Difference (I-J)
Std.
Error
Sig. 95% Confidence Interval
Lower Bound Upper Bound
Caltex
Caltex Woolworths 3.69610* 1.47939 .013 .7918 6.6004
Coles Express -.63847 1.63182 .696 -3.8420 2.5650
7-Eleven 2.94094* 1.25795 .020 .4714 5.4105
Caltex
Woolworths
Caltex -3.69610* 1.47939 .013 -6.6004 -.7918
Coles Express -4.33457* 1.96794 .028 -8.1979 -.4712
7-Eleven -.75516 1.67105 .651 -4.0357 2.5254
Coles
Express
Caltex .63847 1.63182 .696 -2.5650 3.8420
Caltex Woolworths 4.33457* 1.96794 .028 .4712 8.1979
7-Eleven 3.57941* 1.80738 .048 .0313 7.1276
7-Eleven
Caltex -2.94094* 1.25795 .020 -5.4105 -.4714
Caltex Woolworths .75516 1.67105 .651 -2.5254 4.0357
Coles Express -3.57941* 1.80738 .048 -7.1276 -.0313
*. The mean difference is significant at the 0.05 level.
Post hoc comparisons using the Bonferroni test showed that the mean petrol price for the
Caltex Woolworths brand (M = 120.39, SD = 14.82, N = 110) was significantly different
than the Caltex brand (M = 124.08, SD = 14.16, N = 382), p < 0.05. There was significant
difference between the Caltex brand (M = 124.08, SD = 14.16, N = 382) and the 7-
Eleven brand (M = 121.14, SD = 12.00, N = 171), p < 0.05. There was also significant
difference in the mean petrol prices for Caltex Woolworths brand (M = 120.39, SD =
14.82, N = 110) and the Coles Express brand (M = 124.72, SD = 13.05, N = 86), p <
0.05. Lastly, there was significant difference in the mean petrol prices the Coles Express
brand (M = 124.72, SD = 13.05, N = 86) and the 7-Eleven brand (M = 121.14, SD =

12.00, N = 171), p < 0.05. There was however no significant difference in the mean
petrol prices for the Caltex brand (M = 124.08, SD = 14.16, N = 382) and the Coles
Express brand (M = 124.72, SD = 13.05, N = 86), p > 0.05. Also there was no significant
difference in the mean petrol prices for the 7-Eleven brand (M = 121.14, SD = 12.00, N =
171) and the Caltex Woolworths brand (M = 120.39, SD = 14.82, N = 110), p > 0.05.
Based on the above results and analysis, it is evident that Caltex Woolworths brand has
the lowest average petrol prices among the four brands that were considered (M = 120.39,
SD = 14.82, N = 110).
4. Section 4: Collect and analysis Dataset 2
A sample of 50 KOI students was selected and the students were asked on which of the
service station they prefer to buy petrol. Results showed that majority (40.0%, n = 20) of
the students interviewed preferred Caltex Woolworths. See table 10 below
Table 10: Frequency table
Service station Frequency (n) Percent (%)
7-Eleven 10 20
BP 9 18
Caltex 11 22
Caltex Woolworths 20 40
Total 50 100

The least preferred service station by the sampled students was the BP (18.0%, n = 9).
Caltex had a preference of 22.0% (n = 11) while 7-Eleven had a preference of 20.0% (n =
10).
Figure 3: Bar chart of service station preference
5. Discussion and conclusion
The aim of this study was to analyze the petrol prices in Australia. Different approaches
were utilized in the analysis process. First, two data types were used for analysis. The
first dataset was a secondary dataset that comprised of historical fuel prices for the
different brands in 2016. This data set had 1000 cases. The second dataset was a
primary dataset collected from the KOI students and sought to find out the student’s
preference of service stations when it comes to buying petrol. This second dataset had 50
cases. Results from the first dataset showed that the average fuel prices in all the petrol
stations was 122.50. Further analysis revealed that Caltex Woolworths was the cheapest
of the selected four service stations. The most expensive was the Coles Express. From

dataset 2, the study established that most students prefer fueling at Caltex Woolworths
while the least BP was the least preferred service station among the sampled students.
These results reveal very interesting findings which are crucial for policy making. Future
research should have focus on a larger sample size to get the views of the students on
which of the service stations they would prefer. The sample area for future research
should extend to more than one university in order to obtain more representative results.
References
ACCC, 2018. Petrol prices are not the same: report on petrol prices by major retailer in 2017.
May.pp. 1-46. Retrieved May 10, 2019, from https://www.accc.gov.au/system/files/1411_Report
%20on%20petrol%20prices%20in%202017_FA.pdf